The Issue with Floating Point

In a python REPL environment, we would see the following:

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>>> x = 0.1
>>> format(x, '.32f')
'0.10000000000000000555111512312578'

That is x is not actually stored as 0.1. This is because \(\dfrac{1}{10}\) cannot be represented as a finite combination of these:

\[ \dfrac{a_1}{2} + \dfrac{a_2}{2^2} + \dfrac{a_3}{2^3} + \cdots . \]

In other words, there is no corresponding binary fraction for 0.1.

Which of the following can be expressed without any error as a floating point?

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